Total Positivity

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Part of the Springer Series in Statistics book series (SSS)


The theory of totally positive matrices and functions has its origins in work of Pólya (1913, 1915). Such matrices and functions were in- vestigated by I. Schoenberg in a series of beautiful papers starting in 1930. Much early history of the subject can be found in later papers of Schoenberg (1951, 1953).


Probability Density Function Hazard Rate Positive Function Exponential Family Frequency Function 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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